├── J.m
├── J_1.m
├── README.md
├── main.m
└── pexit.m


/J.m:
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 1 | function [j]=J(theta)
 2 | % JFunction is an approximated function for PEXIT curves of AWGN
 3 | % channel model, it takes alpha vector and returns a corresponding
 4 | % JFunction vector.
 5 | % Values are arbitary that fullfill required function
 6 | [m,n]=size(theta);
 7 | j=zeros(m,n);
 8 | theta_a=1.6363;
 9 | aj1=-0.0421061;
10 | bj1=0.209252;
11 | cj1=-0.00640081;
12 | aj2=0.00181491;
13 | bj2=-0.142675;
14 | cj2=-0.0822054;
15 | dj2=0.0549608;
16 | for p=1:m
17 |     for q=1:n
18 |         if 0<=theta(p,q)&&theta(p,q)<theta_a
19 |             j(p,q)=aj1*theta(p,q)^3+bj1*theta(p,q)^2+cj1*theta(p,q);
20 |         else
21 |             if theta_a<theta(p,q)&&theta(p,q)<10
22 |                 j(p,q)=1-exp(aj2*theta(p,q)^3+bj2*theta(p,q)^2+cj2*theta(p,q)+dj2);
23 |             else
24 |                 j(p,q)=1;
25 |             end
26 |         end
27 |     end
28 | end
29 | end


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/J_1.m:
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 1 | function [theta]=J_1(I)
 2 | % JInverseFunction is an approximated function for EXIT curves of
 3 | % BEC channel model, it takes mutual information vector and returns
 4 | % a corresponding JInverseFunction vector.
 5 | % Values are arbitary that fullfill inverse of Jfunction above
 6 | [m,n]=size(I);
 7 | theta=zeros(m,n);
 8 | I_a=0.3646;
 9 | at1=1.09542;
10 | bt1=0.214217;
11 | ct1=2.33727;
12 | at2=0.706692;
13 | bt2=0.386013;
14 | ct2=-1.75017;
15 | for i=1:m
16 |     for j=1:n
17 |         if 0<=I(i,j)&&I(i,j)<=I_a
18 |             theta(i,j)=at1*I(i,j).^2+bt1*I(i,j)+ct1*sqrt(I(i,j));
19 |         else
20 |             if I(i,j)~=1
21 |                 theta(i,j)=-at2*log(bt2*(1-I(i,j)))-ct2*I(i,j);
22 |             else
23 |                 theta(i,j)=1000;
24 |             end
25 |         end
26 |     end
27 | end


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/README.md:
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1 | # Protograph_EXIT_chart
2 | The GitHub repository includes a simple MATLAB implementation of PEXIT charts for estimating the iterative decoding threshold of Low-Density Parity-Check (LDPC) codes based on mutual information. This implementation is based on the article "Protograph LDPC Codes Design Based on EXIT Analysis" by G. Liva and M. Chiani, published in the IEEE Global Telecommunications Conference in 2007.
3 | 
4 | The repository contains the necessary code to implement PEXIT charts and estimate the iterative decoding threshold of LDPC codes.
5 | 


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/main.m:
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 1 | %Copyright(c) 2012, USAtyuk Vasiliy 
 2 | %All rights reserved.
 3 | %
 4 | %Redistribution and use in source and binary forms, with or without
 5 | %modification, are permitted provided that the following conditions are met :
 6 | %*Redistributions of source code must retain the above copyright
 7 | %notice, this list of conditions and the following disclaimer.
 8 | %* Redistributions in binary form must reproduce the above copyright
 9 | %notice, this list of conditions and the following disclaimer in the
10 | %documentation and / or other materials provided with the distribution.
11 | %* Neither the name of the <organization> nor the
12 | %names of its contributors may be used to endorse or promote products
13 | %derived from this software without specific prior written permission.
14 | %
15 | %THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
16 | %ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
17 | %WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
18 | %DISCLAIMED.IN NO EVENT SHALL <COPYRIGHT HOLDER> BE LIABLE FOR ANY
19 | %DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
20 | %(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
21 | %LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
22 | %ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
23 | %(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
24 | %SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
25 | 
26 | function [midEN, SNR]=MET_LDPC_treshold(S,R,pun)
27 | 
28 | S=[1 1 1 1 1 1;
29 |    0 1 1 1 1 1;
30 |    0 0 1 1 1 1;
31 | 	];
32 |     iterations=250;%number of decoding iterations
33 | 	pun=[6]; %puncture nodes
34 | 	samples=25;%number of samples(Monte Carlo) to make smooth estimation of iterative decoding treshold
35 | 	leEN=0;
36 | 	riEN=2;
37 |     [m n]=size(S);
38 | 	R=(n-m)/(n-length(pun));
39 | 
40 | 
41 | 
42 | 
43 | while( ~pexit(S,riEN,R,pun,iterations))
44 |     leEN=riEN;
45 |     riEN=riEN+1;
46 | %     disp(num2str(riEN))
47 | end
48 | for L=1:1:samples 
49 |     midEN=(riEN+leEN)/2;
50 | %     disp(num2str(midEN))
51 | %     if pexit(S,midEN,R)
52 |     if pexit(S,midEN,R,pun,iterations)
53 |         riEN=midEN;
54 |     else
55 |         leEN=midEN;
56 |     end
57 | end
58 | midEN=(riEN+leEN)/2; %Eb/No
59 | SNR = midEN + 10*log10(log2(4)*R); %SNR for QPSK log2(M), M=4
60 | end
61 | 
62 | 


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/pexit.m:
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 1 | 
 2 | function [a]=pexit(B,ENdb,R,pun,iter)
 3 | % function [a]=pexit(B,EN,R)
 4 | [m,n]=size(B);
 5 | L=iter;
 6 | EN=10^(ENdb/10);
 7 | cch2=8*R*EN*ones(1,n);
 8 | cch2(pun)=0;
 9 | IEv=zeros(m,n);
10 | IEc=zeros(m,n);
11 | IEc(:,pun)=1;
12 | %L=1000;%number of iterations
13 | Iapp=zeros(1,n);
14 | Iapp(pun)=1;
15 | store_Iapp=zeros(1,n);
16 | a=false;
17 | for k=1:L
18 |     for j=1:n;
19 |         temp=J_1(IEc(:,j)).^2;
20 |         for i=1:m
21 |             if B(i,j)==0
22 |                 IEv(i,j)=0;
23 |                 continue;
24 |             else
25 |                 IEv(i,j)=J(sqrt(B(:,j)'*temp-temp(i)+cch2(j)));
26 |             end
27 |         end
28 |     end
29 |     for i=1:m
30 |         temp=J_1(1-IEv(i,:))'.^2;
31 |         for j=1:n
32 |             if B(i,j)==0
33 |                 IEc(i,j)=0;
34 |                 continue;
35 |             else
36 |                 IEc(i,j)=1-J(sqrt(B(i,:)*temp-temp(j)));
37 |             end
38 |         end
39 |     end
40 |     Iapp=J(sqrt(sum(B.*(J_1(IEc).^2))+cch2));
41 |      Iapp(pun)=1;
42 |     if all(Iapp>=1-(1e-5))%&&all(Iapp<=1+1e-5)
43 |         a=true;
44 |         return;
45 |     else
46 |         eIapp=store_Iapp-Iapp;
47 |         if all((eIapp)<1e-5)&&all((eIapp)>-(1e-5))
48 |             a=false;
49 |             return
50 |         else
51 |             store_Iapp=Iapp;
52 |         end
53 |     end
54 |      
55 | end


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